A copper refinery produces a copper ingot weighing 70 kg. If the copper is drawn into wire whose diameter is 7.50 mm, how many meters of copper can be obtained from the ingot? The density of copper is 8.94 g/cm³. (Assume that the wire is a cylinder whose volume V = πr²h, where r is its radius and h is its height or length.)

Video transcript

Hi everyone here we have a question that says gold wire is used in computer chips to bond as it enables a smooth and under interrupted flow of electricity. Consider producing gold wire with a 0.1 millimeter diameter from a gold bar that weighs 12.4 kg, calculate the length in meters of the wire. That would be produced given the density of gold is 19.3 g per centimeter cube. Assume that the wire is in the shape of the cylinder, volume equals pi r squared times height where r equals radius and age equals height. So our diameter Equals 0.01 mm. So our radius is that divided by two, which is 0.005 mm Which equals 0. cm. Our density is 19. grams per centimeters cubed And our mass is 12. kilograms, Which is 12,400 g. Our density equals mass over volume. And we're going to substitute volume for our volume equation. So density equals mass over pi r squared times height. So we're going to rearrange that to give us high equals in over p pi R squared. So our height equals 12,400 g Divided by 19. grams per centimeter cube Times Pi. So we're going to use 3. Time 0. cm squared. So our height equals 8. times 10 to the 8th cm Or 8.18 times to the six m. And that is our final answer. Thank you for watching Bye!